Newtonian helicopter model

Abstract

In recent years, there has been growing interest within the control community on the subject of construction and control of autonomous model helicopters and experimental helicopter platforms [66, 90, 103, 119]. It appears that the classical modelling and control approaches (cf. [87]) are not directly applicable due to the high actuation to inertia ratios and the highly non-linear nature of the rotation dynamics exploited in desired flight conditions for scale model autonomous helicopters. This has led the community to develop an idealised non-linear dynamic model for a scale model autonomous helicopter (cf. conference papers [28, 62, 90, 95, 101, 103, 119] and more recently the journal papers [93, 102]). Although the model that is becoming standard in the literature does not contain a sophisticated aerodynamic analysis and concerns only the basic dynamic states of the helicopter, it is hoped that by resolving the basic trajectory planning and control issues, it will be possible to extend these developments to provide robust practical controllers for scale model autonomous helicopters. The key technical difficulty encountered is the the presence of significant small body forces [12, 116] leading to weakly non-minimum phase zero dynamics for the full dynamic model [47]. This is a theoretical problem that was also encountered in the investigation of the control of a vertical take-off and landing jet (VTOL) [31, 35, 67, 73, 115] and [91, pg. 246.]. Unfortunately, the differential Flatness technics applicable in the case of a VTOL do not apply in general to a helicopter [53, 64, 66, 116]. Recent work [102, 119] exploits the partial differential Flatness properties that do exist for the helicopter model, however, the final stabilizing control design still relies on an approximation of the model. Most other authors have applied a robust control design to the model obtained by ignoring the small body forces and later analyzing the performance of the system to ensure that for desired trajectories, the unmodelled dynamics do not destroy the stability of the closed-Ioop system [28, 62, 71, 93]. Such results either take the form of monitoring the behaviour of the system in order to ascertain when the stability guarantees of the control design are broken (cf. Lemma 15.1) or provide some apriori guarantees for a restricted class of trajectories [28, 61, 93].

The authors of this chapte r are Robert Mahony, Tarek Hamei, Alejandro Dzul and Rogelio Lozano . R. Mahony is with th e Department of Electrical & Computer Systems Engineering, Monash University, Clayton, Victoria , 3800, Australia. T. Hamel is with th e Cemif, Universit e d’Evry, 40 rue du Pelvoux , CE 1455 Courcouro nnes, Franc e. A. Dzul and R. Lozano are with the Laboratory Heudiasyc, UTC UMR CNRS 6599, Centre de Recherche de Royalli eu , BP 20529, 60205 Compiegne Cedex , France.